Java/src/main/java/com/thealgorithms/stacks/PrefixToInfix.java

package com.thealgorithms.stacks;

import java.util.Stack;

/**
 * Converts a prefix expression to an infix expression using a stack.
 *
 * The input prefix expression should consist of
 * valid operands (letters or digits) and operators (+, -, *, /, ^).
 * Parentheses are not required in the prefix string.
 */
public final class PrefixToInfix {
    private PrefixToInfix() {
    }

    /**
     * Determines if a given character is a valid arithmetic operator.
     *
     * @param token the character to check
     * @return true if the character is an operator, false otherwise
     */
    public static boolean isOperator(char token) {
        return token == '+' || token == '-' || token == '/' || token == '*' || token == '^';
    }

    /**
     * Converts a valid prefix expression to an infix expression.
     *
     * @param prefix the prefix expression to convert
     * @return the equivalent infix expression
     * @throws NullPointerException     if the prefix expression is null
     */
    public static String getPrefixToInfix(String prefix) {
        if (prefix == null) {
            throw new NullPointerException("Null prefix expression");
        }
        if (prefix.isEmpty()) {
            return "";
        }

        Stack<String> stack = new Stack<>();

        // Iterate over the prefix expression from right to left
        for (int i = prefix.length() - 1; i >= 0; i--) {
            char token = prefix.charAt(i);

            if (isOperator(token)) {
                // Pop two operands from stack
                String operandA = stack.pop();
                String operandB = stack.pop();

                // Form the infix expression with parentheses
                String infix = "(" + operandA + token + operandB + ")";

                // Push the resulting infix expression back onto the stack
                stack.push(infix);
            } else {
                // Push operand onto stack
                stack.push(Character.toString(token));
            }
        }

        if (stack.size() != 1) {
            throw new ArithmeticException("Malformed prefix expression");
        }

        return stack.pop(); // final element on the stack is the full infix expression
    }
}